The present invention relates in general to pH control, and in particular to a new and useful method and apparatus of utilizing an estimation for a pH titration curve in the adaptive control of pH.
The control of pH is important to many processes including: boiler water treatment, chemical and biological reaction, municipal waste digestion, acid pickling/etching processes, cooling tower water treatment, electrohydrolysis, coagulation/precipitation processes, chemical reactor feeds and wastewater neutralization. Waste water treatment is especially difficult because composition is unknown and varies with time.
The control of pH is a very difficult problem. The titration curve is a plot showing pH that results from adding a given proportion of reagent. The source of the difficulty of pH control is the result of two major factors: The nonlinearity of the titration curve at any particular point in time and the time variation in the shape of the titration curve as the influent composition changes. The influent flow rate, concentrations of various acids, bases and buffering salts, and temperature change with time.
The nonlinearity of the titration curve is most acute for unbuffered acids or bases. For such cases, near a pH of 7 pH units, addition of a relatively small amount of acid or base results in a drastic change in pH. But if the pH is acidic or basic, then relatively large amounts of acid or base result in only small changes in pH. Thus when the pH is near 7 pH units, the process has an extremely high gain and when the process is not near a pH of 7 pH units, the process gain is quite small. Over the normal range of operation with strong acids or bases, it is not unexpected to have the process gain change by a factor of 10,000,000,000. Because proportional-integral (PI) controllers assume that the process is linear, the application of a classical PI controller for pH control is usually ineffective.
Because of the difficulty of pH control, many schemes include large blending volumes, batch processing, or continual operator involvement and are economically expensive.
Proposals have been made for a nonlinear PID pH controller which utilized a deadband about pH of 7 pH units and a different controller gain outside the deadband. While this controller represents an improvement over PID control for neutralization, it suffers from three major limitations: (1) it is designed only for neutralization, (2) at low buffering, it is difficult to fit the highly nonlinear pH function with such a simple function, and (3) most importantly, as the shape of the titration curve changes due to changes in acid and buffering salt composition, this method would require retuning although no provisions for tuning on-line are given.
U.S. Pat. No. 3,899,294 discloses a method for titration curve identification by simply titrating a slip stream of the main effluent stream. Then the titration curve is used to select the reagent flow rate to attain the desired pH. This procedure is relatively expensive since an automated titration system must be used to obtain the titration curve. In addition, the titration time for such an automated system may be significant in comparison to the fluid residence time in the process; therefore, when composition changes of the process stream occur, the analytical dead-time will reduce the effectiveness of the controller.
In some ways, pH control is a very simple process with a single input, a single output and easily modeled first order linear dynamics. A reagent stream is added to the incoming process stream, the two streams are mixed, and the pH is measured. The proper pH is achieved by adding the proper proportion of reagent.
What makes things so difficult is the process gain. The gain is extremely nonlinear and may change drastically if the process composition changes slightly. The gain may be so high that the output pH is hopelessly sensitive to tiny errors in the control effort. A general purpose pH controller must handle all three problems: nonlinear gain, time-varying gain, and extremely high gain.